Variable-range Projection Model for Turbulence-driven Collisions

TL;DR

This paper presents a new model for the distribution of relative velocities of inertial particles in turbulent flows, which impacts collision rates relevant to planet formation.

Contribution

It introduces a variable-range projection model explaining the velocity distribution with a specific exponential form, supported by simulations and analytical solutions.

Findings

Distribution follows P(ΔV) ∼ exp(-C |ΔV|^{4/3})

Model aligns with numerical simulations

Results inform collision rates in planet formation

Abstract

We discuss the probability distribution of relative speed $\Delta V$ of inertial particles suspended in a highly turbulent gas when the Stokes numbers, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution $P(\Delta V) \sim \exp(-C |\Delta V|^{4/3})$ (for some constant $C$). Our conclusions are supported by numerical simulations and the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesised mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.